Relevant bibliographies by topics / Algebraic normal form

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  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers
  6. Reports

Academic literature on the topic 'Algebraic normal form'

Author: Grafiati
Published: 4 June 2021
Last updated: 30 January 2023

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Journal articles on the topic "Algebraic normal form"

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Vardasbi, Ali, Mahmoud Salmasizadeh, and Javad Mohajeri. "Superpoly algebraic normal form monomial test on Trivium." IET Information Security 7, no. 3 (September 1, 2013): 230–38. http://dx.doi.org/10.1049/iet-ifs.2012.0175.

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Trenn, Stephan. "A normal form for pure differential algebraic systems." Linear Algebra and its Applications 430, no. 4 (February 2009): 1070–84. http://dx.doi.org/10.1016/j.laa.2008.10.004.

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Gazor, Majid, and Mahsa Kazemi. "Normal Form Analysis of ℤ2-Equivariant Singularities." International Journal of Bifurcation and Chaos 29, no. 02 (February 2019): 1950015. http://dx.doi.org/10.1142/s0218127419500159.

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Singular parametric systems usually experience bifurcations when their parameters slightly vary around certain critical values, that is, surprising changes occur in their dynamics. The bifurcation analysis is important due to their applications in real world problems. Here, we provide a brief review of the mathematical concepts in the extension of our developed Maple library, Singularity, for the study of [Formula: see text]-equivariant local bifurcations. We explain how the process of this analysis is involved with algebraic objects and tools from computational algebraic geometry. Our procedures for computing normal forms, universal unfoldings, local transition varieties and persistent bifurcation diagram classifications are presented. Finally, we consider several Chua circuit type systems to demonstrate the applicability of our Maple library. We show how Singularity can be used for local equilibrium bifurcation analysis of such systems and their possible small perturbations. A brief user interface of [Formula: see text]-equivariant extension of Singularity is also presented.
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Bakoev, Valentin. "Fast Bitwise Implementation of the Algebraic Normal Form Transform." Serdica Journal of Computing 11, no. 1 (November 27, 2017): 45–57. http://dx.doi.org/10.55630/sjc.2017.11.45-57.

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The representation of Boolean functions by their algebraic normalforms (ANFs) is very important for cryptography, coding theory andother scientific areas. The ANFs are used in computing the algebraic degreeof S-boxes, some other cryptographic criteria and parameters of errorcorrectingcodes. Their applications require these criteria and parameters tobe computed by fast algorithms. Hence the corresponding ANFs should alsobe obtained by fast algorithms. Here we continue our previous work on fastcomputing of the ANFs of Boolean functions. We present and investigatethe full version of bitwise implementation of the ANF transform. The experimental results show that this implementation ismore than 25 times faster in comparison to the well-known byte-wise ANFtransform.ACM Computing Classification System (1998): F.2.1, F.2.2.
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Reissig, G. "Semi-implicit differential-algebraic equations constitute a normal form." IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications 42, no. 7 (July 1995): 399–402. http://dx.doi.org/10.1109/81.401157.

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Gilkey, Peter, and Raina Ivanova. "The Jordan normal form of Osserman algebraic curvature tensors." Results in Mathematics 40, no. 1-4 (October 2001): 192–204. http://dx.doi.org/10.1007/bf03322705.

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Gauthier, Yvon. "On Cantor's normal form theorem and algebraic number theory." International Journal of Algebra 12, no. 3 (2018): 133–40. http://dx.doi.org/10.12988/ija.2018.8413.

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Talwar, S., N. Sri Namachchivaya, and P. G. Voulgaris. "Approximate Feedback Linearization: A Normal Form Approach." Journal of Dynamic Systems, Measurement, and Control 118, no. 2 (June 1, 1996): 201–10. http://dx.doi.org/10.1115/1.2802305.

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The emerging field of nonlinear control theory has attempted to alleviate the problem associated with applying linear control theory to nonlinear problems. A segment of nonlinear control theory, called exact feedback linearization, has proven useful in a class of problems satisfying certain controllability and integrability constraints. Approximate feedback linearization has enlarged this class by weakening the integrability conditions, but application of both these techniques remains limited to problems in which a series of linear partial differential equations can easily be solved. By use of the idea of normal forms, from dynamical systems theory, an efficient method of obtaining the necessary coordinate transformation and nonlinear feedback rules is given. This method, which involves the solution of a set of linear algebraic equations, is valid for any dimensional system and any order nonlinearity provided it meets the approximate feedback linearization conditions.
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GAZOR, MAJID, and PEI YU. "INFINITE ORDER PARAMETRIC NORMAL FORM OF HOPF SINGULARITY." International Journal of Bifurcation and Chaos 18, no. 11 (November 2008): 3393–408. http://dx.doi.org/10.1142/s0218127408022445.

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In this paper, we introduce a suitable algebraic structure for efficient computation of the parametric normal form of Hopf singularity based on a notion of formal decompositions. Our parametric state and time spaces are respectively graded parametric Lie algebra and graded ring. As a consequence, the parametric state space is also a graded module. Parameter space is observed as an integral domain as well as a vector space, while the near-identity parameter map acts on the parametric state space. The method of multiple Lie bracket is used to obtain an infinite order parametric normal form of codimension-one Hopf singularity. Filtration topology is revisited and proved that state, parameter and time (near-identity) maps are continuous. Furthermore, parametric normal form is a convergent process with respect to filtration topology. All the results presented in this paper are verified by using Maple.
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Chand Gupta, Kishan, and Palash Sarkar. "Computing Walsh Transform from the Algebraic Normal Form of a Boolean Function." Electronic Notes in Discrete Mathematics 15 (May 2003): 92–96. http://dx.doi.org/10.1016/s1571-0653(04)00542-6.

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Dissertations / Theses on the topic "Algebraic normal form"

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Calik, Cagdas. "Computing Cryptographic Properties Of Boolean Functions From The Algebraic Normal Form Representation." Phd thesis, METU, 2013. http://etd.lib.metu.edu.tr/upload/12615759/index.pdf.

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Boolean functions play an important role in the design and analysis of symmetric-key cryptosystems, as well as having applications in other fields such as coding theory. Boolean functions acting on large number of inputs introduces the problem of computing the cryptographic properties. Traditional methods of computing these properties involve transformations which require computation and memory resources exponential in the number of input variables. When the number of inputs is large, Boolean functions are usually defined by the algebraic normal form (ANF) representation. In this thesis, methods for computing the weight and nonlinearity of Boolean functions from the ANF representation are investigated. The relation between the ANF coecients and the weight of a Boolean function was introduced by Carlet and Guillot. This expression allows the weight to be computed in $mathcal{O}(2^p)$ operations for a Boolean function containing p monomials in its ANF. In this work, a more ecient algorithm for computing the weight is proposed, which eliminates the unnecessary calculations in the weight expression. By generalizing the weight expression, a formulation of the distances to the set of linear functions is obtained. Using this formulation, the problem of computing the nonlinearity of a Boolean function from its ANF is reduced to an associated binary integer programming problem. This approach allows the computation of nonlinearity for Boolean functions with high number of input variables and consisting of small number of monomials in a reasonable time.
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Mus, Koksal. "An Alternative Normal Form For Elliptic Curve Cryptography: Edwards Curves." Master's thesis, METU, 2009. http://etd.lib.metu.edu.tr/upload/12611065/index.pdf.

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A new normal form x2 + y2 = c2(1 + x2y2) of elliptic curves was introduced by M. Harold Edwards in 2007 over the field k having characteristic different than 2. This new form has very special and important properties such that addition operation is strongly unified and complete for properly chosen parameter c . In other words, doubling can be done by using the addition formula and any two points on the curve can be added by the addition formula without exception. D. Bernstein and T. Lange added one more parameter d to the normal form to cover a large class of elliptic curves, x2 + y2 = c2(1 + dx2y2) over the same field. In this thesis, an expository overview of the literature on Edwards curves is given. First, the types of Edwards curves over the nonbinary field k are introduced, addition and doubling over the curves are derived and efficient algorithms for addition and doubling are stated with their costs. Finally, known elliptic curves and Edwards curves are compared according to their cryptographic applications. The way to choose the Edwards curve which is most appropriate for cryptographic applications is also explained.
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Chen, Yahao. "Geometric analysis of differential-algebraic equations and control systems : linear, nonlinear and linearizable." Thesis, Normandie, 2019. http://www.theses.fr/2019NORMIR04.

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Dans la première partie de cette thèse, nous étudions les équations différentielles algébriques (en abrégé EDA) linéaires et les systèmes de contrôles linéaires associés (en abrégé SCEDA). Les problèmes traités et les résultats obtenus sont résumés comme suit : 1. Relations géométriques entre les EDA linéaires et les systèmes de contrôles génériques SCEDO. Nous introduisons une méthode, appelée explicitation, pour associer un SCEDO à n'importe quel EDA linéaire. L'explicitation d'une EDA est une classe des SCEDO, précisément un SCEDO défini, à un changement de coordonnées près, une transformation de bouclage près et une injection de sortie près. Puis nous comparons les « suites de Wong » d'une EDA avec les espaces invariants de son explicitation. Nous prouvons que la forme canonique de Kronecker FCK d'une EDA linéaire et la forme canonique de Morse FCM d'un SCEDO, ont une correspondance une à une et que leurs invariants sont liés. De plus, nous définissons l'équivalence interne de deux EDA et montrons sa particularité par rapport à l'équivalence externe en examinant les relations avec la régularité interne, i.e., l'existence et l'unicité de solutions. 2. Transformation d'un SCEDA linéaire vers sa forme canonique via la méthode d'explicitation avec des variables de driving. Nous étudions les relations entre la forme canonique par bouclage FCFB d'un SCEDA proposée dans la littérature et la forme canonique de Morse pour les SCEDO. Premièrement, dans le but de relier SCEDA avec les SCEDO, nous utilisons une méthode appelée explicitation (avec des variables de driving). Cette méthode attache à une classe de SCEDO avec deux types d'entrées (le contrôle original et le vecteur des variables de driving) à un SCEDA donné. D'autre part, pour un SCEDO linéaire classique (sans variable de driving) nous proposons une forme de Morse triangulaire FMT pour modifier la construction de la FCM. Basé sur la FMT nous proposons une forme étendue FMT et une forme étendue de FCM pour les SCEDO avec deux types d'entrées. Finalement, un algorithme est donné pour transformer un SCEDA dans sa FCFB. Cet algorithme est construit sur la FCM d'un SCEDO donné par la procédure d'explicitation. Un exemple numérique illustre la structure et l'efficacité de l'algorithme. Pour les EDA non linéaires et les SCEDA (quasi linéaires) nous étudions les problèmes suivants : 3. Explicitations, analyse externe et interne et formes normales des EDA non linéaires. Nous généralisons les deux procédures d'explicitation (avec ou sans variables de driving) dans le cas des EDA non linéaires. L'objectif de ces deux méthodes est d'associer un SCEDO non linéaire à une EDA non linéaire telle que nous puissions l'analyser à l'aide de la théorie des EDO non linéaires. Nous comparons les différences de l'équivalence interne et externe des EDA non linéaires en étudiant leurs relations avec l'existence et l'unicité d'une solution (régularité interne). Puis nous montrons que l'analyse interne des EDA non linéaire est liée à la dynamique nulle en théorie classique du contrôle non linéaire. De plus, nous montrons les relations des EDAS de forme purement semi-explicite avec les 2 procédures d'explicitations. Finalement, une généralisation de la forme de Weierstrass non linéaire FW basée sur la dynamique nulle d'un SCEDO non linéaire donné par la méthode d'explicitation est proposée
In the first part of this thesis, we study linear differential-algebraic equations (shortly, DAEs) and linear control systems given by DAEs (shortly, DAECSs). The discussed problems and obtained results are summarized as follows. 1. Geometric connections between linear DAEs and linear ODE control systems ODECSs. We propose a procedure, named explicitation, to associate a linear ODECS to any linear DAE. The explicitation of a DAE is a class of ODECSs, or more precisely, an ODECS defined up to a coordinates change, a feedback transformation and an output injection. Then we compare the Wong sequences of a DAE with invariant subspaces of its explicitation. We prove that the basic canonical forms, the Kronecker canonical form KCF of linear DAEs and the Morse canonical form MCF of ODECSs, have a perfect correspondence and their invariants (indices and subspaces) are related. Furthermore, we define the internal equivalence of two DAEs and show its difference with the external equivalence by discussing their relations with internal regularity, i.e., the existence and uniqueness of solutions. 2. Transform a linear DAECS into its feedback canonical form via the explicitation with driving variables. We study connections between the feedback canonical form FBCF of DAE control systems DAECSs proposed in the literature and the famous Morse canonical form MCF of ODECSs. In order to connect DAECSs with ODECSs, we use a procedure named explicitation (with driving variables). This procedure attaches a class of ODECSs with two kinds of inputs (the original control input and the vector of driving variables) to a given DAECS. On the other hand, for classical linear ODECSs (without driving variables), we propose a Morse triangular form MTF to modify the construction of the classical MCF. Based on the MTF, we propose an extended MTF and an extended MCF for ODECSs with two kinds of inputs. Finally, an algorithm is proposed to transform a given DAECS into its FBCF. This algorithm is based on the extended MCF of an ODECS given by the explication procedure. Finally, a numerical example is given to show the structure and efficiency of the proposed algorithm. For nonlinear DAEs and DAECSs (of quasi-linear form), we study the following problems: 3. Explicitations, external and internal analysis, and normal forms of nonlinear DAEs. We generalize the two explicitation procedures (with or without driving variable) proposed in the linear case for nonlinear DAEs of quasi-linear form. The purpose of these two explicitation procedures is to associate a nonlinear ODECS to any nonlinear DAE such that we can use the classical nonlinear ODE control theory to analyze nonlinear DAEs. We discuss differences of internal and external equivalence of nonlinear DAEs by showing their relations with the existence and uniqueness of solutions (internal regularity). Then we show that the internal analysis of nonlinear DAEs is closely related to the zero dynamics in the classical nonlinear control theory. Moreover, we show relations of DAEs of pure semi-explicit form with the two explicitation procedures. Furthermore, a nonlinear generalization of the Weierstrass form WE is proposed based on the zero dynamics of a nonlinear ODECS given by the explicitation procedure
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Millan, William L. "Analysis and design of Boolean functions for cryptographic applications." Thesis, Queensland University of Technology, 1997.

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Cheng, Howard. "Algorithms for Normal Forms for Matrices of Polynomials and Ore Polynomials." Thesis, University of Waterloo, 2003. http://hdl.handle.net/10012/1088.

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In this thesis we study algorithms for computing normal forms for matrices of Ore polynomials while controlling coefficient growth. By formulating row reduction as a linear algebra problem, we obtain a fraction-free algorithm for row reduction for matrices of Ore polynomials. The algorithm allows us to compute the rank and a basis of the left nullspace of the input matrix. When the input is restricted to matrices of shift polynomials and ordinary polynomials, we obtain fraction-free algorithms for computing row-reduced forms and weak Popov forms. These algorithms can be used to compute a greatest common right divisor and a least common left multiple of such matrices. Our fraction-free row reduction algorithm can be viewed as a generalization of subresultant algorithms. The linear algebra formulation allows us to obtain bounds on the size of the intermediate results and to analyze the complexity of our algorithms. We then make use of the fraction-free algorithm as a basis to formulate modular algorithms for computing a row-reduced form, a weak Popov form, and the Popov form of a polynomial matrix. By examining the linear algebra formulation, we develop criteria for detecting unlucky homomorphisms and determining the number of homomorphic images required.
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Ramos, Alberto Gil Couto Pimentel. "Numerical solution of Sturm–Liouville problems via Fer streamers." Thesis, University of Cambridge, 2016. https://www.repository.cam.ac.uk/handle/1810/256997.

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The subject matter of this dissertation is the design, analysis and practical implementation of a new numerical method to approximate the eigenvalues and eigenfunctions of regular Sturm–Liouville problems, given in Liouville’s normal form, defined on compact intervals, with self-adjoint separated boundary conditions. These are classical problems in computational mathematics which lie on the interface between numerical analysis and spectral theory, with important applications in physics and chemistry, not least in the approximation of energy levels and wave functions of quantum systems. Because of their great importance, many numerical algorithms have been proposed over the years which span a vast and diverse repertoire of techniques. When compared with previous approaches, the principal advantage of the numerical method proposed in this dissertation is that it is accompanied by error bounds which: (i) hold uniformly over the entire eigenvalue range, and, (ii) can attain arbitrary high-order. This dissertation is composed of two parts, aggregated according to the regularity of the potential function. First, in the main part of this thesis, this work considers the truncation, discretization, practical implementation and MATLAB software, of the new approach for the classical setting with continuous and piecewise analytic potentials (Ramos and Iserles, 2015; Ramos, 2015a,b,c). Later, towards the end, this work touches upon an extension of the new ideas that enabled the truncation of the new approach, but instead for the general setting with absolutely integrable potentials (Ramos, 2014).
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Darpö, Erik. "Problems in the Classification Theory of Non-Associative Simple Algebras." Doctoral thesis, Uppsala universitet, Matematiska institutionen, 2009. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-9536.

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In spite of its 150 years history, the problem of classifying all finite-dimensional division algebras over a field k is still unsolved whenever k is not algebraically closed. The present thesis concerns some different aspects of this problem, and the related problems of classifying all composition and absolute valued algebras. A tripartition of the class of all fields is given, based on the dimensions in which division algebras over a field exist. Moreover, all finite-dimensional flexible real division algebras are classified. This class includes in particular all finite-dimensional commutative real division algebras, of which two different classifications, along different lines, are presented. It is shown that every vector product algebra has dimension zero, one, three or seven, and that its isomorphism type is determined by its adherent quadratic form. This yields a new and elementary proof for the corresponding, classical result for unital composition algebras. A rotation in a Euclidean space is an orthogonal map that locally acts as a plane rotation with a fixed angle. All pairs of rotations in finite-dimensional Euclidean spaces are classified up to orthogonal similarity. A description of all composition algebras having an LR-bijective idempotent is given. On the basis of this description, all absolute valued algebras having a one-sided unity or a non-zero central idempotent are classified.
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Chakir, El-Alaoui El-Houcine. "Les métriques sous riemanniennes en dimension 3." Rouen, 1996. http://www.theses.fr/1996ROUES055.

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Cette thèse est consacrée essentiellement à l'étude des métriques sous-riemanniennes dites de contact en dimension 3. Bien que cette étude soit faite localement, on observe des différences fondamentales avec les métriques riemanniennes. En particulier, les lieux conjugue et cut d'un point p contiennent p dans leur adhérence. Ce travail se divise en deux parties : 1. On montre, dans un premier temps, qu'on peut associer à toute métrique sous-riemannienne de contact formelle une forme normale formelle. Ensuite, dans un deuxième temps, on montre que cette forme normale est actuellement lisse (i. E. C, c) si la métrique l'est. Aussi, cette forme normale permet de définir des invariants associés aux métriques sous-riemanniennes de contact. 2. A l'aide de cette forme normale on prouve que l'application exponentielle d'une métrique sous-riemannienne de contact générique est déterminée par un certain jet fini de la métrique. Et on en déduit une classification générique de ces singularités (i. E. Lieux conjugués).
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Linfoot, Andy James. "A Case Study of A Multithreaded Buchberger Normal Form Algorithm." Diss., The University of Arizona, 2006. http://hdl.handle.net/10150/305141.

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Groebner bases have many applications in mathematics, science, and engineering. This dissertation deals with the algorithmic aspects of computing these bases. The dissertation begins with a brief introduction of fundamental concepts about Groebner bases. Following this a discussion of various implementation issues are discussed. Much of the practical difficulties of using Groebner basis algorithms and techniques stems from the high computational complexity. It is shown that the algorithmic complexity of computing a Groebner basis primarily stems from the calculation of normal forms. This is established by studying run profiles of various computations. This leads to two options of making Groebner basis techniques more practical. They are to reduce the complexity by developing new algorithms (heuristics) or reduce running time of normal form calculations by introducing concurrency. The later approach is taken in the remainder of the dissertation where a multithreaded normal form algorithm is presented and discussed. It is shown with a simple example that the new algorithm demonstrates a speedup and scalability. The algorithm also has the advantage of being completion strategy independent. We conclude with an outline of future research involving the new algorithm.
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Hartsell, Jack. "A Normal Form for Words in the Temperley-Lieb Algebra and the Artin Braid Group on Three Strands." Digital Commons @ East Tennessee State University, 2018. https://dc.etsu.edu/etd/3504.

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The motivation for this thesis is the computer-assisted calculation of the Jones poly- nomial from braid words in the Artin braid group on three strands, denoted B3. The method used for calculation of the Jones polynomial is the original method that was created when the Jones polynomial was first discovered by Vaughan Jones in 1984. This method utilizes the Temperley-Lieb algebra, and in our case the Temperley-Lieb Algebra on three strands, denoted A3, thus generalizations about A3 that assist with the process of calculation are pursued.
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Books on the topic "Algebraic normal form"

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Manichev, Vladimir, Valentina Glazkova, and Кузьмина Анастасия. Numerical methods. The authentic and exact solution of the differential and algebraic equations in SAE systems of SAPR. ru: INFRA-M Academic Publishing LLC., 2016. http://dx.doi.org/10.12737/13138.

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In the manual classical numerical methods are considered and algorithms for the decision of systems of the ordinary differential equations (ODE), nonlinear and linear algebraic equations (NAU and LAU), and also ways of ensuring reliability and demanded accuracy of results of the decision. Ideas, which still not are stated are reflected in textbooks on calculus mathematics, namely: decision systems the ODE without reduction to a normal form of Cauchy resolved rather derivative, and refusal from any numerical an equivalent - nykh of transformations of the initial equations of mathematical models and is- the hodnykh of data because such transformations can change properties of models at a variation of coefficients in corresponding urav- neniyakh. It is intended for students, graduate students and teachers of higher education institutions in the direction of preparation "Informatics and computer facilities". The grant will also be useful for engineers and scientists on the corresponding specialties.
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Aleksani︠a︡n, A. A. Dizʺi︠u︡nktivnye normalʹnye formy nad lineĭnymi funkt︠s︡ii︠a︡mi: Teorii︠a︡ i prilozhenii︠a︡. Erevan: Izd-vo Erevanskogo universiteta, 1990.

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Zbigniew, Hajto, ed. Algebraic groups and differential Galois theory. Providence, R.I: American Mathematical Society, 2011.

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Ninul, Anatolij Sergeevič. Tenzornaja trigonometrija: Teorija i prilozenija / Theory and Applications /. Moscow, Russia: Mir Publisher, 2004.

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Ninul, Anatolij Sergeevič. Tensor Trigonometry. Moscow, Russia: Fizmatlit Publisher, 2021.

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Dufour, Jean-Paul, and Nguyen Tien Zung. Poisson Structures and Their Normal Forms. Springer London, Limited, 2006.

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Bokut, Leonid, Yuqun Chen, and Kyriakos Kalorkoti. Grobner-Shirshov Bases: Normal Forms, Combinatorial and Decision Problems in Algebra. World Scientific Publishing Co Pte Ltd, 2018.

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M¨uhlherr, Bernhard, Holger P. Petersson, and Richard M. Weiss. Quadratic Forms of Type E6, E7 and E8. Princeton University Press, 2017. http://dx.doi.org/10.23943/princeton/9780691166902.003.0008.

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This chapter presents various results about quadratic forms of type E⁶, E₇, and E₈. It first recalls the definition of a quadratic space Λ‎ = (K, L, q) of type Eℓ for ℓ = 6, 7 or 8. If D₁, D₂, and D₃ are division algebras, a quadratic form of type E⁶ can be characterized as the anisotropic sum of two quadratic forms, one similar to the norm of a quaternion division algebra D over K and the other similar to the norm of a separable quadratic extension E/K such that E is a subalgebra of D over K. Also, there exist fields of arbitrary characteristic over which there exist quadratic forms of type E⁶, E₇, and E₈. The chapter also considers a number of propositions regarding quadratic spaces, including anisotropic quadratic spaces, and proves some more special properties of quadratic forms of type E₅, E⁶, E₇, and E₈.
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Poisson Structures and Their Normal Forms (Progress in Mathematics). Birkhauser, 2005.

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Silva, Rapti Manohara De. Two spectral theorems: The Jordan canonical form for linear operators and the spectral theorem for normal operators. 1988.

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Book chapters on the topic "Algebraic normal form"

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Kauers, Manuel, and Jakob Moosbauer. "A Normal Form for Matrix Multiplication Schemes." In Algebraic Informatics, 149–60. Cham: Springer International Publishing, 2022. http://dx.doi.org/10.1007/978-3-031-19685-0_11.

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Della Dora, J., and L. Stolovitch. "Poincare normal form and carleman linearization." In Algebraic Computing in Control, 288–306. Berlin, Heidelberg: Springer Berlin Heidelberg, 1991. http://dx.doi.org/10.1007/bfb0006946.

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Mourrain, B. "A New Criterion for Normal Form Algorithms." In Applied Algebra, Algebraic Algorithms and Error-Correcting Codes, 430–42. Berlin, Heidelberg: Springer Berlin Heidelberg, 1999. http://dx.doi.org/10.1007/3-540-46796-3_41.

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Poinsot, Laurent. "Linear Induction Algebra and a Normal Form for Linear Operators." In Algebraic Informatics, 260–73. Berlin, Heidelberg: Springer Berlin Heidelberg, 2013. http://dx.doi.org/10.1007/978-3-642-40663-8_24.

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Mano, Ken, and Mizuhito Ogawa. "Unique normal form property of Higher-Order Rewriting Systems." In Algebraic and Logic Programming, 269–83. Berlin, Heidelberg: Springer Berlin Heidelberg, 1996. http://dx.doi.org/10.1007/3-540-61735-3_18.

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Çalık, Çağdaş, and Ali Doğanaksoy. "Computing the Weight of a Boolean Function from Its Algebraic Normal Form." In Lecture Notes in Computer Science, 89–100. Berlin, Heidelberg: Springer Berlin Heidelberg, 2012. http://dx.doi.org/10.1007/978-3-642-30615-0_8.

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Roch, J. L., and G. Villard. "Parallel computations with algebraic numbers a case study: Jordan normal form of matrices." In PARLE'94 Parallel Architectures and Languages Europe, 701–12. Berlin, Heidelberg: Springer Berlin Heidelberg, 1994. http://dx.doi.org/10.1007/3-540-58184-7_142.

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Guilloud, Simon, and Viktor Kunčak. "Equivalence Checking for Orthocomplemented Bisemilattices in Log-Linear Time." In Tools and Algorithms for the Construction and Analysis of Systems, 196–214. Cham: Springer International Publishing, 2022. http://dx.doi.org/10.1007/978-3-030-99527-0_11.

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AbstractMotivated by proof checking, we consider the problem of efficiently establishing equivalence of propositional formulas by relaxing the completeness requirements while still providing certain guarantees. We present a quasilinear time algorithm to decide the word problem on a natural algebraic structures we call orthocomplemented bisemilattices, a subtheory of Boolean algebra. The starting point for our procedure is a variation of Aho, Hopcroft, Ullman algorithm for isomorphism of trees, which we generalize to directed acyclic graphs. We combine this algorithm with a term rewriting system we introduce to decide equivalence of terms. We prove that our rewriting system is terminating and confluent, implying the existence of a normal form. We then show that our algorithm computes this normal form in log linear (and thus sub-quadratic) time. We provide pseudocode and a minimal working implementation in Scala.
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Batteux, Boris. "On the Algebraic Normal Form and Walsh Spectrum of Symmetric Functions over Finite Rings." In Arithmetic of Finite Fields, 92–107. Berlin, Heidelberg: Springer Berlin Heidelberg, 2012. http://dx.doi.org/10.1007/978-3-642-31662-3_7.

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Zhang, Wenying, and Chuan-Kun Wu. "The Algebraic Normal Form, Linear Complexity and k-Error Linear Complexity of Single-Cycle T-Function." In Sequences and Their Applications – SETA 2006, 391–401. Berlin, Heidelberg: Springer Berlin Heidelberg, 2006. http://dx.doi.org/10.1007/11863854_34.

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Conference papers on the topic "Algebraic normal form"

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Liu, Renzhang, and Yanbin Pan. "Computing Hermite Normal Form Faster via Solving System of Linear Equations." In ISSAC '19: International Symposium on Symbolic and Algebraic Computation. New York, NY, USA: ACM, 2019. http://dx.doi.org/10.1145/3326229.3326238.

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Pashinska-Gadzheva, Maria, Valentin Bakoev, Iliya Bouyukliev, and Dushan Bikov. "Optimizations in computing the algebraic normal form transform of Boolean functions." In 2021 International Conference Automatics and Informatics (ICAI). IEEE, 2021. http://dx.doi.org/10.1109/icai52893.2021.9639777.

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Wang, Dingkang, Hesong Wang, and Fanghui Xiao. "An extended GCD algorithm for parametric univariate polynomials and application to parametric smith normal form." In ISSAC '20: International Symposium on Symbolic and Algebraic Computation. New York, NY, USA: ACM, 2020. http://dx.doi.org/10.1145/3373207.3404019.

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Dogaru, Ioana, and Radu Dogaru. "Algebraic normal form for rapid prototyping of elementary hybrid cellular automata in FPGA." In 2010 3rd International Symposium on Electrical and Electronics Engineering (ISEEE). IEEE, 2010. http://dx.doi.org/10.1109/iseee.2010.5628500.

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Zhu, Huibiao, Yongxin Zhao, and Jifeng He. "Locality-Based Normal Form Approach to Linking Algebraic Semantics and Operational Semantics for an Event-Driven System-Level Language." In 2009 Australian Software Engineering Conference. IEEE, 2009. http://dx.doi.org/10.1109/aswec.2009.20.

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Wong, M. M., and M. L. D. Wong. "A high throughput low power compact AES S-box implementation using composite field arithmetic and Algebraic Normal Form representation." In 2010 2nd Asia Symposium on Quality Electronic Design (ASQED 2010). IEEE, 2010. http://dx.doi.org/10.1109/asqed.2010.5548317.

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Butcher, Eric A., and S. C. Sinha. "On the Analysis of Time-Periodic Nonlinear Hamiltonian Dynamical Systems." In ASME 1995 Design Engineering Technical Conferences collocated with the ASME 1995 15th International Computers in Engineering Conference and the ASME 1995 9th Annual Engineering Database Symposium. American Society of Mechanical Engineers, 1995. http://dx.doi.org/10.1115/detc1995-0277.

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Abstract In this paper, some analysis techniques for general time-periodic nonlinear Hamiltonian dynamical systems have been presented. Unlike the traditional perturbation or averaging methods, these techniques are applicable to systems whose Hamiltonians contain ‘strong’ parametric excitation terms. First, the well-known Liapunov-Floquet (L-F) transformation is utilized to convert the time-periodic dynamical system to a form in which the linear pan is time invariant. At this stage two viable alternatives are suggested. In the first approach, the resulting dynamical system is transformed to a Hamiltonian normal form through an application of permutation matrices. It is demonstrated that this approach is simple and straightforward as opposed to the traditional methods where a complicated set of algebraic manipulations are required. Since these operations yield Hamiltonians whose quadratic parts are integrable and time-invariant, further analysis can be carried out by the application of action-angle coordinate transformation and Hamiltonian perturbation theory. In the second approach, the resulting quasilinear time-periodic system (with a time-invariant linear part) is directly analyzed via time-dependent normal form theory. In many instances, the system can be analyzed via time-independent normal form theory or by the method of averaging. Examples of a nonlinear Mathieu’s equation and coupled nonlinear Mathieu’s equations are included and some preliminary results are presented.
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Couceiro, Miguel, Nicolas Hug, Henri Prade, and Gilles Richard. "Behavior of Analogical Inference w.r.t. Boolean Functions." In Twenty-Seventh International Joint Conference on Artificial Intelligence {IJCAI-18}. California: International Joint Conferences on Artificial Intelligence Organization, 2018. http://dx.doi.org/10.24963/ijcai.2018/284.

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It has been observed that a particular form of analogical inference, based on analogical proportions, yields competitive results in classification tasks. Using the algebraic normal form of Boolean functions, it has been shown that analogical prediction is always exact iff the labeling function is affine. We point out that affine functions are also meaningful when using another view of analogy. We address the accuracy of analogical inference for arbitrary Boolean functions and show that if a function is epsilon-close to an affine function, then the probability of making a wrong prediction is upper bounded by 4 epsilon. This result is confirmed by an empirical study showing that the upper bound is tight. It highlights the specificity of analogical inference, also characterized in terms of the Hamming distance.
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Makaryan, Vahagn, Michael Sutton, Tatevik Yeghiazaryan, Davresh Hasanyan, and Xiaomin Deng. "Cracked Elastic Layer Under a Compressive Mechanical Load." In ASME 2009 International Mechanical Engineering Congress and Exposition. ASMEDC, 2009. http://dx.doi.org/10.1115/imece2009-11967.

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In the present work, the problem of an elastic layer weakened by a finite penny shaped crack parallel to a layer’s surface that is loaded in compression is considered. Assuming that the surfaces of the crack have frictional slipping contact, Henkel and Legendre integral transformation techniques are employed to formulate solutions in the form of an infinite system of linear algebraic equations. The regularity of the equations is established and closed-form solutions are obtained for stresses and strains. Assuming shear stress on the crack surfaces is linearly distributed, numerical results show both geometric and physical parameters have an essential influence on the stress distribution around the crack, with specific parameter values indicating the normal stress along the crack surface can change its sign from negative to positive. The implications of the work will be discussed.
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Dai, Jian S. "Characteristics of the Screw Transformation Matrix and Their Effect on Chasles’ Motion." In ASME 2011 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2011. http://dx.doi.org/10.1115/detc2011-48613.

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Rigid body displacement can be presented with Chasles’ motion by rotating about an axis and translating along the axis. This motion can be implemented by a screw transformation matrix in the form of either 3×3 dual number matrix or 6×6 transformation matrix that is executed with rotation and translation. This paper investigates characteristics of the screw transformation matrix, and decomposes the dual part of the transformation matrix into the part with an equivalent translation due to the effect of moving rotation axis and the part resulting from a pure translation. New results are presented and new formulae are generated. The analysis further reveals two new traces of the transformation matrix and presents the relation between the screw transformation matrix and the instantaneous screw, leading to the understanding of Chasles’ motion embedded in a normal body transformation. An algebraic and geometric interpretation of the screw transformation matrix is thus given, presenting an intrinsic property of the screw transformation matrix in relation to the finite screw. The paper ends with a case study to verify the theory and illustrate the principle.
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Reports on the topic "Algebraic normal form"

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Baader, Franz, Silvio Ghilardi, and Cesare Tinelli. A New Combination Procedure for the Word Problem that Generalizes Fusion Decidability Results in Modal Logics. Technische Universität Dresden, 2003. http://dx.doi.org/10.25368/2022.130.

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Previous results for combining decision procedures for the word problem in the non-disjoint case do not apply to equational theories induced by modal logics - which are not disjoint for sharing the theory of Boolean algebras. Conversely, decidability results for the fusion of modal logics are strongly tailored towards the special theories at hand, and thus do not generalize to other types of equational theories. In this paper, we present a new approach for combining decision procedures for the word problem in the non-disjoint case that applies to equational theories induced by modal logics, but is not restricted to them. The known fusion decidability results for modal logics are instances of our approach. However, even for equational theories induced by modal logics our results are more general since they are not restricted to so-called normal modal logics.
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